Do the Math – How Many Ancestors Do I Have?

Sometimes you just need a simple answer to the question:

How many ancestors do I have?

There’s a mathematical formula for figuring out how many ancestors you have at each generation.

x=2n

x is the number of direct-line, biological ancestors you have;

n is the generation back from you.

So, one generation back, x=2¹ or x=2, you have 2 ancestors, your biological parents. You may also have adopted parents, step-parents, etc, but for the purpose of DNA matches, we’re concerned with biological ancestors you may have inherited DNA from. As a general rule, this formula shows the largest number of ancestors you could have.

At some point, you’ll have pedigree collapse and this formula no longer applies, but it works well for the limited number of generations we examine in most of our family history work.

If you want to know how many ancestors you have, just add up the number from each generation, so parents (2) + grandparents (4) + great-grandparents (8) = 14 ancestors within 3 generations, etc. Again, at some point, cousins married cousins and you’ll have some level of great-grandparent (the same person) who shows up in your tree (as an ancestor) multiple times, so this formula isn’t perfect, but it’s great for most purposes.

Why do you care how many ancestors you have?

You may care for several reasons.

First, you may be building a free family tree but be limited by the site to 100 names. You need an estimate of how many generations you’re going to be able to add to your tree. To go back 6 generations, you need a tree with 126 names in addition to your name. (21 + 22 + 23 + 24 + 25 + 26 = 126 or 2 + 4 + 8 + 16 + 32 + 64 = 126.) If you’re using a site that only allows 100 names, you need to be aware you can only completely include 5 generations back or 62 names plus yours.

Second, and this is me, today, you may be building a descendancy tree and you’re trying to figure a realistic goal for which generation, n, you’ll start with. I’m using Ancestral Quest Basics (free) to download someone’s descendancy tree from FamilySearch (free). At first, I was ambitious and thought, ‘Oh, I’ll go back 10 generations.’ But in order to have the program build the descendancy tree, I have to select each person in that 10th generation and wait for the program to download the data (and it takes the program a long time if there are a lot of descendants). Using the formula, x = 210, I realized I was dealing with 1,024 ancestors in just the 10th generation. Even if I only downloaded info for the husband (and risked missing other relationships from the wife), I’d be at 512 individuals. Not gonna happen! After doing the math, I lowered my goal considerably.

Third, you may want to know how big a DNA puzzle is before you try to solve it. When you see a DNA match, with an estimated relationship, you want a general idea of how many ancestors you need to examine to find your match. If the estimated relationship is 1st cousins, that’s pretty simple, your common ancestor is most likely one or more grandparents and you have 4 possibilities. The number grows exponentially the more distant your relationship.

Below is a MyHeritage DNA estimated relationship chart for a match they think is a 3rd to 5th cousin.* The chart shows our most recent common ancestor could be anywhere from a great-grandparent to a 4th great-grandparent. We don’t always guesstimate correctly when we’re trying to figure out how many people we’re talking about. When you do the math, you find there are 120 possible common ancestors.

At our closest, this person may be my 2nd cousin some generations removed. This would make our common ancestor a great-grandparent. Using the formula above, this would be x=2³, and I have at most 8 possibilities for this most recent common ancestor. At our most distant, we may share a 4th great-grandparent, or x=26, and I have 64 possibilities. Now I have to add up the possibilities at each generation, so 8 + 16 + 32 + 64 = 120 total possible common ancestors. That’s a lot of people to consider. It helps to know the size of the problem before you set out to solve it.

Anyway, it’s a bit technical, but sometimes I quickly do the math to assess the work required to solve a problem and this is a great go-to formula to assess the number of ancestors we’re dealing with. Best with your research!

*And sometimes the real relationship falls outside the bounds of the estimated relationship. The estimated relationship is just a hint for where you should start looking.

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